Now that you've answered what the oldest casino in Las Vegas is (great answer, by the way), how about the oldest casino in Reno?
Though Reno's early wide-open gambling history is as extensive as Las Vegas's, almost all of the original casinos are gone. Harold's Club (1935), Harrah's (1937, originally as a bingo parlor), the Nevada Club (1946) are defunct.
That leaves the Nugget in Sparks (not technically Reno, but certainly part of the metro area) as the oldest. It opened in 1955 as Dick Graves' Nugget. John Ascuaga bought it in 1960; he was the general manager at the time. The Ascuaga family owned and operated it until finally selling out to Global Gaming in late 2013 for a price that has never been disclosed.
In Reno proper, the oldest casino is the Club Cal Neva, which opened in 1962. Though it has taken over, operated, and closed or sold nearby hotel towers over the years, today, it's still pretty much the same as it was 60 years ago: 35,000 square feet in a two-story building with slots, table games, and a race and sports book, plus the venerable Top Deck restaurant, the 24/7 coffee shop now called the Casino Grill, and the Sports Grill next to the sports book.
For those who haven't been there, if you're driving east, you can't really tell any difference -- i.e., when you're leaving Reno and entering Sparks. Besides driving under US 395 -- very noticeable, but not the city limits -- the only way to determine which town you're in is by the nondescript street signs ("entering Sparks", or "entering Reno").